• 대한수학회논문집
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• 제26권1호
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• pp.37-49
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• 2011

We investigate the asymptotic equivalence for linear differential systems by means of the notions of $t_{\infty}$-similarity and strong stability.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.445-451
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• 2003

In this paper we study asymptotic equivalence between linear differential system x' = A(t)x and its perturbed system y' = A(t)y(y) + g(t).

• Computers and Concrete
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• 제7권4호
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• pp.317-329
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• 2010

The paper describes localization of deformation in a bar under tensile loading. The material of the bar is considered as non-linear viscous elastic and the bar consists of two symmetric halves. It is assumed that the model represents behavior of the quasi-brittle viscous material under uniaxial tension with different loading rates. Besides that, the bar could represent uniaxial stress-strain law on a single plane of a microplane material model. Non-linear material property is taken from the microplane material model and it is coupled with the viscous damper producing non-linear Maxwell material model. Mathematically, the problem is described with a system of two partial differential equations with a non-linear algebraic constraint. In order to obtain solution, the system of differential algebraic equations is transformed into a system of three partial differential equations. System is subjected to loadings of different rate and it is shown that localization occurs only for high loading rates. Mathematically, in such a case two solutions are possible: one without the localization (unstable) and one with the localization (stable one). Furthermore, mass is added to the bar and in that case the problem is described with a system of four differential equations. It is demonstrated that for high enough loading rates, it is the added mass that dominates the response, in contrast to the viscous and elastic material parameters that dominated in the case without mass. This is demonstrated by several numerical examples.

• Journal of information and communication convergence engineering
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• 제2권3호
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• pp.187-192
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• 2004

A method using two dimension Haar functions approximation for solving the problem of a partial differential equation and estimating the parameters of a non-linear distributed parameter system (DPS) is presented. The applications of orthogonal functions, including Haar functions, and their transforms have been given much attention in system control and communication engineering field since 1970's. The Haar functions set forms a complete set of orthogonal rectangular functions similar in several respects to the Walsh functions. The algorithm adopted in this paper is that of estimating the parameters of non-linear DPS by converting and transforming a partial differential equation into a simple algebraic equation. Two dimension Haar functions approximation method is introduced newly to represent and solve a partial differential equation. The proposed method is supported by numerical examples for demonstration the fast, convenient capabilities of the method.

• 대한수학회지
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• 제34권2호
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• pp.407-426
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• 1997

We consider a system of perturbed linear differential equation x' =A(t)x + f(t,x) and obtain conditions to ensure the strong-equiasymptotic stability of the zero solution.

• 충청수학회지
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• 제27권3호
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• pp.495-502
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• 2014

In this paper, we show the ${\psi}$-uniform stability for linear impulsive differential equations and their perturbations by using the impulsive Gronwall's inequalities.

• 대한수학회지
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• 제53권5호
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• pp.1019-1036
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• 2016

In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the non-linear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.

• 대한전자공학회논문지TC
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• 제49권5호
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• pp.37-43
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• 2012

LTE 시스템에서는 폐회로 기반의 다중 안테나 기술이 적용되었으며, 차분 코드북을 비롯한 다양한 다중 안테나 기반의 선부호화 기술들이 향상된 LTE (LTE-Advanced) 시스템의 요구조건을 만족시키기 위해 제안되었다. 차분 코드북 설계와 관련하여 이전에 연구된 내용은 준 대각(quasi-diagonal) 단위 행렬 및 구면 캡(spherical cap)에 중점을 두었지만, 이는 동 이득 성질을 만족하지 못한다. 동 이득 성질은 특히 상향 링크에서 첨두 전력 대 평균 전력비 (PAPR)에 상당한 영향을 미치므로 매우 중요하다. 본 논문에서는 각 송신 안테나에 동 이득을 유지하는 성질을 이용한 새로운 차분 코드북을 상향 링크 기반 차분 선부호화 시스템에 적용하고, 이를 통해 비트 오류율(BER)과 첨두 전력 대 평균 전력비를 분석하였다. 특히, 송신기의 비선형 증폭기를 고려하여 다양한 차분 선부호화 기법들의 성능을 분석하였다. 모의 실험을 통해 선형 증폭기를 고려할 경우 기존에 제안된 차분 코드북이 우수한 성능을 보이지만, 비선형 증폭기를 고려할 경우에는 제안하는 차분 코드북의 우수함을 증명하였다.

• 대한수학회논문집
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• 제31권3호
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• pp.603-611
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• 2016

In this paper, we show that if $\mathcal{A}$ is a differential subalgebra of Banach algebras $\mathcal{B}({\ell}^r)$, $1{\leq}r{\leq}{\infty}$, then solutions of the infinite dimensional linear system associated with a matrix in $\mathcal{A}$ have its p-exponential stability being equivalent to each other for different $1{\leq}p{\leq}{\infty}$.

• 호남수학학술지
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• 제24권1호
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$